Hmmm, input here from someone with a Degree in Professional (be warned - this could be dangerous! lol)
First of all, unless you clearly define which is past and which is present regarding tense - never mix the two. It is just too jarring. I definitely commend your ambition in trying it, but ... if you're only just starting out (and it sounds like you are), I wouldn't do it. And this is why. You tend to get a lot of would-be writers who will "discover" something that sounds cool and then they'll just focus on that alone because it's cool and it sounds artsy-fartsy fancy. In reality, they end up sounding like overly pretentious try-hards that no-one takes seriously. There's a reason why so many authors tend to stick to the past tense - it's the easiest to master. As the saying goes - if it ain't broke ....
Secondly, fluff. Add more of it!!!!! Trust me, you need it. At the moment, it seems like you have same problem I had for years - you're writing is thread-bare. You have dialogue, extremely basic descriptors and that's it. Surprisingly, what helped me to get out of that - nasty - habit was the two script-writing modules we had to do in my degree. How, you might ask? Well, script-writing is as thread-bare as writing can get. So what you need to do is add in all of the surprisingly necessary fluff. Descriptors, thoughts, feelings. All of this can tell story just as much if not moreso than the dialogue can. However, there is a thin line between just enough and too much. Robert Jordan - too much. Stephen King - just enough. Even Tolkien just enough.
A few other little pointers. Watch your use of grammar. Yes, at this stage, you are still in the first draft stage. But still.... Do not be afraid to apply the editor's scalpel to you're own work. A writer with an analytical mind is their own worst enemy and best friend at the same time (once you can get your head around that, you'll be right). As you edit drafts, do not be surprised if your story changes. It sounds to me like your something of an organic writer - meaning you have no real definitive plan on where the story is going - or you do, you just don't have an itinary/plot. That's okay. I'm the same (so is Stephen King, by the way). Trust me, having no plot or even no idea where the hell your story is going it will seem frustrating and even scary at times, but in the end, it is exciting and rewarding. Just follow your gut because that's the inspiration... be careful of impinging on other, pre-existing works. You mentioned an element of time-travel in this story. Just be aware, there are already some pre-existing works - H.G. Wells "The Time Machine" and "Doctor Who" come to mind immediately. I know there are a few others out there, I'm must - admittedly - not sure of what they are. Time-Travel is a lot more complicated than what people may think. If you're talking about constantly leaping in the one direction - say forward in time - then you can effectively create a timeline. If, however, you have time-travel operate both ways, a lot of research is involved. And I mean, a lot of research. This is in order to make the past historically accurate. And to make the future more believable. Doctor Who has been around since 1962/63. With over 15 incarnations now, how many times has the doctor been walking down a London Street, likely remembering something that happened on that same street who-knows-when?
I'm not saying all of this to discourage you from exploring writing. Far from it. Write. Write your heart out. Even if you never publish anything, just write. Just please promise me this one thing - do not become a Robert Jordan or a Stephen Donaldson. Robert Jordan refused to acknowledge that his readers had any imagination of their own and he would dictate what people had to see - big no-no. Stephen Donaldson .... poorly constructed and developed characters who barely two-dimensional at best; plots that were just as bad and because he's a former high level barrister, he would through in the occasional word that only someone with an elite law degree would have any chance of knowing!!! Pretentious!! Another big no-no.
Final word, as you go on and further develop as a writer, you will find your own voice. But until then, do not be afraid to take advice from others. You're already asking for feedback, so that is a good start.
Absolute final word - I promise!!!!! lol ha ha. Language. More specifically, the use and form of it. A lot of artsy literature critics even now say Stephen King has a "Tin-ear" for language because he writes how normal people speak. There's nothing Hoi-poloi about his writing. 50 years and how many #1 Best sellers? Gee, maybe people like it when a writer understands how they talk. I'm getting somewhere with this. I'm working on something of my own that has been rolling around for about 16 or so years now (and probably equally as many edits). This is totally organic, meaning all I had was an urge to write - no direction, nothing else but this feeling of a story. One thing that has come out of it that has stood out to me has been the use and form of language. Mainly, how I've used form of language to differentiate groups of people. Story in a nutshell is this - a group of four related kids set out from their home of town of Cooma (Australia, my home country) on a camping trip while the first harvest of the year is happening. Oh, yeah, this is set well into the future - post a mega ice-age. Things happen that mean the kids never return to Cooma and are pursued through the south-western tablelands of NSW. Now, the kids all speak a form of English that is proper and formal. Their pursuers use a form of English that is nigh-on piratical - the leader of the bandits (a real slimeball if there ever was one) moreso than those he leads. In the town of Hay the kids meet a community of Androids who use a form of English that is much like we use today. Now, this wasn't anything deliberate on my behalf - it just happened organically - but it works. When we first meet the leader of the bandits, we know from his very first words that he is of a lower societal cast than the kids and we also get at inclination that he is possibly a villian (spoiler - he is!!!) My point being - form of language can be a useful tool, if you know how to use it.
Apologies for the long reply. Yes, I am a writer. lol